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Lecture_Notes_02 - University of Toronto ECE316 Fall 2011...

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University of Toronto ECE316 Fall 2011 CommunicaƟon Systems September 12, 2011 L ãçÙ NÊã Ý #2 Instructor: Ivo Maljević 2 Signals and Signal Space Electrical signals in communicaƟon systems represent informaƟon/data (e.g., voice, video, music, etc.). In this course, signals will be funcƟons of either conƟnuous Ɵme variable t (e.g., g ( t ) , x ( t ) , etc.) or funcƟons of discrete Ɵme (e.g., g ( nT ) , x ( nT ) , etc.). Systems generally modify signal either to shape it for beƩer transmission/recepƟon (e.g, filters, equalizers), or to extract various parameters (e.g., Ɵme delay, frequency, distance of the target/user, etc.). More details on linear systems will be given in chapter 3. 2.1 Size of a Signal In class, we went over a definiƟon of a signal energy as its squared norm in L 2 space. We also stated what the signal nees to saƟsfy to have a finite norm. To illustrate the necessary condiƟon for the existence of the energy integral, we solved an example where g ( t ) = e - a | t | , where a > 0 is some constant.
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